htg%SSKJr SSKJrJrJrJrJrJrJ r SSK J r SSK r SSK Jr SSKJr SSKrSSKrSSKrSSKJr SSKJr /SQrS(S jr\\\rS \S '\\\S 4rS \S '\\\4r S \S'\RB\RDr!S \S'S)Sjr#\"SS9S*Sj5r$"SS5r%"SS\ RL5r'S+S,Sjjr(S-Sjr)S.Sjr*S/Sjr+"SS\'5r,S0Sjr-S.Sjr.S1S jr/S2S3S!jjr0S2S4S"jjr1S5S#jr2"S$S%\'5r3S6S&jr4S7S'jr5g)8) annotations)IterableTupleListSequenceAnycastOptional) TypeAliasN) lru_cache)repeat) USE_C_EXT)MatrixSolvernumpy_vector_solvernumpy_matrix_solver NumpySolvertridiagonal_vector_solvertridiagonal_matrix_solverdetect_banded_matrixcompact_banded_matrixBandedMatrixLU banded_matrixquadratic_equationcubic_equationbinomial_coefficientc'D# [U6Hn[U5v M g7fN)ziplist)argses C/var/www/html/env/lib/python3.13/site-packages/ezdxf/math/linalg.py zip_to_listr$,s $Z1g s r MatrixData.FrozenMatrixDataShapeNDArrayc [U[5(a URnUVVs/sHoVs/sHn[U5PM snPM snn$s snfs snnfr isinstancermatrixfloat)Arowvs r#copy_float_matrixr17sF!V HH/0 1qs #s!U1Xs #q 11 # 1s AA AA)maxsizecX:a [S5$[R"U5n[R"U5n[R"X- 5n[X$U-- 5$)zComputes the binomial coefficient (denoted by `k choose i`). Please see the following website for details: http://mathworld.wolfram.com/BinomialCoefficient.html Args: k: size of the set of distinct elements i: size of the subsets r)r-math factorial)kik_facti_factk_i_facts r#rr=sQ uQx..#F..#FNN15)H f,- ..c\rSrSrSrSrS%S&SjjrS'SjrS(SjrS)Sjr S)S jr \ S*S j5r \ S+S j5r\ S+S j5r\ S,S j5rS-SjrS-SjrS-SjrS.SjrS.SjrS/S0SjjrS/S0SjjrS1S0Sjjr\S2Sj5rS3SjrS3SjrS4SjrS5SjrS6SjrS7Sjr S7Sjr!S8Sjr"\"r#S8Sjr$\$r%S8S jr&\&r'S4S!jr(S4S"jr)S9S#jr*S$r+g):rTaBasic matrix implementation based :class:`numpy.ndarray`. Matrix data is stored in row major order, this means in a list of rows, where each row is a list of floats. Initialization: - Matrix(shape=(rows, cols)) ... new matrix filled with zeros - Matrix(matrix[, shape=(rows, cols)]) ... from copy of matrix and optional reshape - Matrix([[row_0], [row_1], ..., [row_n]]) ... from Iterable[Iterable[float]] - Matrix([a1, a2, ..., an], shape=(rows, cols)) ... from Iterable[float] and shape .. versionchanged:: 1.2 Implementation based on :class:`numpy.ndarray`. Attributes: matrix: matrix data as :class:`numpy.ndarray` )r,abs_tolNcSUl[R"S[RS9UlUb)[R"U[RS9UlgUc Ub[R "U5Ulgg[ U[5(a>Uc URnURRU5R5Ulg[U5n[R"UVs/sHn[U5PM sn[RS9Ulgs snf![aH UbB[R"[U5[RS9RU5Ulggf=f)N-q=dtype) r?nparrayfloat64r,zerosr+rshapereshapecopyr TypeError)selfitemsrIr,r/s r#__init__Matrix.__init__is $ !xx"**=  ((6Matrix.rows..s1[DGG[srurSs r#rows Matrix.rowss1T[[111r<c[UR5Vs/sHn[URU55PM sn$s snf)zReturn a list of all columns.)rangerpr rz)rMr8s r#cols Matrix.colss2+0+<=+Set row values to a fixed value or from an iterable of floats.zInvalid item countN)r+r-intrpr len ValueErrorr,rMrwrNs r#set_rowMatrix.set_rowsX eeS\ * *5\NTZZ/EU  u: #12 2" Er<c[U[[45(a[U5/UR-n[ U5UR SS2U4'g)zASet column values to a fixed value or from an iterable of floats.N)r+r-rrkr r,rs r#set_colMatrix.set_cols= eeS\ * *5\NTZZ/E $U  AuHr<ch[U[[45(a[[U55n[ US5n[ [ US55n[[[ URUR55U5HupXPRX-X-4'M g![a  gf=f)amSet diagonal values to a fixed value or from an iterable of floats. An `index` of ``0`` specifies the main diagonal, negative values specifies diagonals below the main diagonal and positive values specifies diagonals above the main diagonal. e.g. given a 4x4 matrix: index ``0`` is [00, 11, 22, 33], index ``-1`` is [10, 21, 32] and index ``+1`` is [01, 12, 23] rN) r+r-rr maxabsminrrrkrpr, IndexError)rMrwrN col_offset row_offsetvalues r#set_diagMatrix.set_diags eeS\ * *5<(EeQ- c%m, c$**djj&A BEJLE FK E.0BBCK  s B## B10B1c<[US9nURSS5 U$)z6Returns the identity matrix for configuration `shape`.)rIr?)rr)clsrIrYs r#identityMatrix.identitys!   1cr<cURRS:Xa*[R"U/[RS9Ulg[ U5UR :Xa%[RURU4Ulg[S5e)zAppend a row to the matrix.rrCInvalid item count.N) r,sizerErFrGrrpr_r)rMrNs r# append_rowMatrix.append_rowsa ;;  q ((E7"**=DK Z4:: %%% U 23DK23 3r<cFURRS:Xa:[R"UVs/sHo"/PM sn[RS9Ulg[ U5UR :Xa%[RURU4Ulg[S5es snf)zAppend a column to the matrix.rrCrN) r,rrErFrGrrkc_r)rMrNitems r# append_colMatrix.append_colss ;;  q ((u#=utFu#=RZZPDK Z4:: %%% U 23DK23 3 $>s Bc\UR5nSURRlU$)z@Returns a frozen matrix, all data is stored in immutable tuples.F)rZr,flags writeablerXs r#freeze Matrix.freeze s" MMO#( r<c2[URU5$)zZGet value by (row, col) index tuple, fancy slicing as known from numpy is not supported. )r-r,)rMrs r# __getitem__Matrix.__getitem__s T[[&''r<c X RU'g)zZSet value by (row, col) index tuple, fancy slicing as known from numpy is not supported. NrW)rMrrs r# __setitem__Matrix.__setitem__s " Dr<c[U[5(d [S5eURUR:wa [S5e[ [ R "URUR:H55$)z'Returns ``True`` if matrices are equal.Matrix class required.Matrices have different shapes.)r+rrLrIboolrEallr,rMothers r#__eq__ Matrix.__eq__sX%((45 5 :: $=> >BFF4;;%,,6788r<c .[U[5(d [S5eURUR:wa [S5e[ [ R "[ R"URURURS955$)zReturns ``True`` if matrices are close to equal, tolerance value for comparison is adjustable by the attribute :attr:`Matrix.abs_tol`. rr)atol) r+rrLrIrrEriscloser,r?rs r#rMatrix.isclose'sf %((45 5 :: $=> >BFF2::dkk5<F r<c[U[5(a [URUR-S9$[UR[U5-S9$)zCMatrix addition by another matrix or a float, returns a new matrix.rWr*rs r#__add__Matrix.__add__?s? eV $ $u||!;< <uU|!;< #, 2 44 ("9 V H=H=H,$1r<rcd\rSrSr\R SSj5r\R SSj5rSrg)riicgrrBrMBs r# solve_matrixSolver.solve_matrixj r<cgrrBrs r# solve_vectorSolver.solve_vectornrr<rBNrMatrixData | NDArrayrrrrrr) rrrrabcabstractmethodrrrrBr<r#rris4     r<rc[U5U:a[U5U:aU*4$U*U- 4$[R"US-SU-U-- 5nU*U-SU-- U*U- SU-- 4$![a [ 5s$f=f)zvReturns the solution for the quadratic equation ``a*x^2 + b*x + c = 0``. Returns 0-2 solutions as a tuple of floats. @)rr5sqrtrtuple)abcr? discriminants r#rrss  1v q6G B5LQyyyAA !12 R, 37 +\0AcAg/N OO ws"A%%A<;A<c[U5S:a [XU5$X- nX - nX0- nXD-nUS- nSU-U- S- n SU-U-SU-- SXt--- S- n X-U -n XU --n U S:a[R "U 5n Sn[R "S X-5[R"[X-5U5-n[R "S X- 5[R"[X- 5U5-nUU-nUU- (aU*U-4$US- nU*U-U*U- U*U- 4$[R"U [R "U *5- 5n[R "U *5S-nU[R"US- 5-U- U[R"US[R--S- 5-U- U[R"US [R--S- 5-U- 4$![a [5s$f=f) zzReturns the solution for the cubic equation ``a*x^3 + b*x^2 + c*x + d = 0``. Returns 0-3 solutions as a tuple of floats. rAg@g"@g;@rgK@gUUUUUU?rg@) rrArithmeticErrorr r5r copysignpowacoscospi)r r r dr.rCAAA3QRQQQDsqrtDexpSrSTST_2thsqrtQ2s r#rrs   1v~ %aA. . A A A B SB q2A q1tax #. 0D8A %!)C 1u ACx !  MM#qy )DHHS^S,I I MM#qy )DHHS^S,I I U q5C"H; 8Dbd d   1tyy#& 'B YYr]S F"s(##b(2dgg -455:2dgg -455: ? 7N s G22H H c[R"U[RS9n[R"U[RS9n[[RR X#5S9$)aQSolves the linear equation system given by a nxn Matrix A . x = B by the numpy.linalg.solve() function. Args: A: matrix [[a11, a12, ..., a1n], [a21, a22, ..., a2n], ... [an1, an2, ..., ann]] B: matrix [[b11, b12, ..., b1m], [b21, b22, ..., b2m], ... [bn1, bn2, ..., bnm]] Raises: numpy.linalg.LinAlgError: singular matrix rCrW)rErFrGrrsolve)r.rmat_Amat_Bs r#rrsD HHQbjj )E HHQbjj )E 6 77r<cF[R"U[RS9n[R"UVs/sHn[U5/PM sn[RS9n[ [R "[R RX$555$s snf)aTSolves the linear equation system given by a nxn Matrix A . x = B, right-hand side quantities as vector B with n elements by the numpy.linalg.solve() function. Args: A: matrix [[a11, a12, ..., a1n], [a21, a22, ..., a2n], ... [an1, an2, ..., ann]] B: vector [b1, b2, ..., bn] Raises: numpy.linalg.LinAlgError: singular matrix rC)rErFrGr-r rRrr')r.rr(r0r)s r#rrsg HHQbjj )E HH!,!QuQxj!,BJJ ?E 67 88-sBc6\rSrSrSrSSjrS SjrS SjrSrg) riz5Replaces in v1.2 the :class:`LUDecomposition` solver.cT[R"U[RS9Ulg)NrC)rErFrGr()rMr.s r#rONumpySolver.__init__sXXarzz2 r<c[R"U[RS9n[[RR UR U5S9$)a Solves the linear equation system given by the nxn Matrix A . x = B, right-hand side quantities as nxm Matrix B. Args: B: matrix [[b11, b12, ..., b1m], [b21, b22, ..., b2m], ... [bn1, bn2, ..., bnm]] Raises: numpy.linalg.LinAlgError: singular matrix rCrW)rErFrGrrr'r()rMrr)s r#rNumpySolver.solve_matrixs6"**-RYY__TZZ?@@r<c[R"UVs/sHn[U5/PM sn[RS9n[ [R "[R RURU555$s snf)zSolves the linear equation system given by the nxn Matrix A . x = B, right-hand side quantities as vector B with n elements. Args: B: vector [b1, b2, ..., bn] Raises: numpy.linalg.LinAlgError: singular matrix rC) rErFr-rGr rRrr'r()rMrr0r)s r#rNumpySolver.solve_vectorsYa0a58*a0 CBHHRYY__TZZ?@AA1sB)r(N)r.rrrrr) rrrrrrOrrrrBr<r#rrs?3A Br<rcvUVs/sHn[U5PM snup4n[X4U[U55$s snf)aSolves the linear equation system given by a tri-diagonal nxn Matrix A . x = B, right-hand side quantities as vector B. Matrix A is diagonal matrix defined by 3 diagonals [-1 (a), 0 (b), +1 (c)]. Note: a0 is not used but has to be present, cn-1 is also not used and must not be present. If an :class:`ZeroDivisionError` exception occurs, the equation system can possibly be solved by :code:`BandedMatrixLU(A, 1, 1).solve_vector(B)` Args: A: diagonal matrix [[a0..an-1], [b0..bn-1], [c0..cn-1]] :: [[b0, c0, 0, 0, ...], [a1, b1, c1, 0, ...], [0, a2, b2, c2, ...], ... ] B: iterable of floats [[b1, b1, ..., bn] Returns: list of floats Raises: ZeroDivisionError: singular matrix )r _solve_tridiagonal_matrix)r.rr0r r r s r#rrs88!""1tAw"GA! $Q1d1g 66#s6c UVs/sHn[U5PM snup4n[U[5(d$[UVs/sHn[U5PM snS9nO[[U5nUR[ U5:wa [ S5e[UR5Vs/sHn[X4XX5PM snS9R5$s snfs snfs snf)aHSolves the linear equation system given by a tri-diagonal nxn Matrix A . x = B, right-hand side quantities as nxm Matrix B. Matrix A is diagonal matrix defined by 3 diagonals [-1 (a), 0 (b), +1 (c)]. Note: a0 is not used but has to be present, cn-1 is also not used and must not be present. If an :class:`ZeroDivisionError` exception occurs, the equation system can possibly be solved by :code:`BandedMatrixLU(A, 1, 1).solve_vector(B)` Args: A: diagonal matrix [[a0..an-1], [b0..bn-1], [c0..cn-1]] :: [[b0, c0, 0, 0, ...], [a1, b1, c1, 0, ...], [0, a2, b2, c2, ...], ... ] B: matrix [[b11, b12, ..., b1m], [b21, b22, ..., b2m], ... [bn1, bn2, ..., bnm]] Returns: matrix as :class:`Matrix` object Raises: ZeroDivisionError: singular matrix rWz+Row count of matrices A and B has to match.) r r+rr rkrrrr3r) r.rr0r r r r/matrix_brzs r#rrsB!""1tAw"GA! a q!9q$s)q!9:?~~QFGG CK==?S?C)!7?S ik#!9TsC C$Cc:[U5nS/U-nS/U-nUSnUSU- US'[SU5H3nX(S- U- Xh'XXXh-- nX8XXXS- -- U- XX'M5 [US- SS5HnXX==XhS-XXS---ss'M U$)aSolves the linear equation system given by a tri-diagonal Matrix(a, b, c) . x = r. Matrix configuration:: [[b0, c0, 0, 0, ...], [a1, b1, c1, 0, ...], [0, a2, b2, c2, ...], ... ] Args: a: lower diagonal [a0 .. an-1], a0 is not used but has to be present b: central diagonal [b0 .. bn-1] c: upper diagonal [c0 .. cn-1], cn-1 is not used and must not be present r: right-hand side quantities Returns: vector x as list of floats Raises: ZeroDivisionError: singular matrix rrror)rr) r r r rnugambetjs r#r3r3Hs4VAUQYAuqyC1C Q4#:AaD 1a[q5CdQTCF]"qtaAh&#- AEB # E Q1uX%%$ Hr<c<[X5up#[XU5nXBU4$)a=Transform matrix A into a compact banded matrix representation. Returns compact representation as :class:`Matrix` object and lower- and upper band count m1 and m2. Args: A: input :class:`Matrix` check_all: check all diagonals if ``True`` or abort testing after first all zero diagonal if ``False``. )rr)r. check_allm1m2rYs r#rrqs&"! /FBaR(A "9r<cF^^SUU4SjjnSUU4SjjnU"5U"54$)zReturns lower- and upper band count m1 and m2. Args: A: input :class:`Matrix` check_all: check all diagonals if ``True`` or abort testing after first all zero diagonal if ``False``. c>Sn[STR5H0n[TRU55(aUnM&T(aM/ U$ U$Nrro)rrpanyr~)r@rr.r>s r# detect_m2'detect_banded_matrix..detect_m2sGq!''"A166!9~~Y #  r<c>Sn[STR5H1n[TRU*55(aUnM'T(aM0 U$ U$rC)rrkrDr~)r?rr.r>s r# detect_m1'detect_banded_matrix..detect_m1sIq!''"A1661":Y #  r<rrB)r.r>rErHs`` r#rrs( ; ##r<cURUR:wa [S5e[5n[ USS5H;nS/U-nUR UR U*55 URU5 M= URUR S55 [ SUS-5H:nUR U5nUR S/U-5 URU5 M< U$)zReturns compact banded matrix representation as :class:`Matrix` object. Args: A: matrix to transform m1: lower band count, excluding main matrix diagonal m2: upper band count, excluding main matrix diagonal zSquare matrix required.rr7rro)rkrprLrrextendr~r)r.r?r@rYrrzs r#rrs ww!''122A 2q" eai 1661": S LL 1b1f ffQi C519 S Hr<cJ\rSrSrSrS Sjr\S Sj5rS SjrS Sjr Sr g) riz9Represents a LU decomposition of a compact banded matrix.c[n[(aSSKJn [ U5Ul[ U5UlU"URUR UR 5uUlUl Ul g)Nr) lu_decompose) _lu_decomposerezdxf.acc.np_supportrNrr?r@r,upperlowerrw)rMr.r?r@rNs r#rOBandedMatrixLU.__init__sL$ 9 92w2w-9!((DGGTWW-U* DJ r<c4URRS$ri)rQrIrSs r#rkBandedMatrixLU.nrowsszz""r<c L[n[(aSSKJn [R "U[R S9n[U5UR:wa [S5e[U"X0RURURURUR55$)Solves the linear equation system given by the banded nxn Matrix A . x = B, right-hand side quantities as vector B with n elements. Args: B: vector [b1, b2, ..., bn] Returns: vector as list of floats r)solve_vector_banded_matrixrC;Item count of vector B has to be equal to matrix row count.)_solve_vector_banded_matrixrrPrXrErFrGrrkrr rQrRrwr?r@)rMrrXxs r#rBandedMatrixLU.solve_vectors}&A" 9 GXXarzz2 q6TZZ M  &::tzz4::tww   r<c[US9nURUR:wa [S5e[UR5Vs/sHo0R U5PM snS9R 5$s snf)a  Solves the linear equation system given by the banded nxn Matrix A . x = B, right-hand side quantities as nxm Matrix B. Args: B: matrix [[b11, b12, ..., b1m], [b21, b22, ..., b2m], ... [bn1, bn2, ..., bnm]] Returns: matrix as :class:`Matrix` object rWz,Row count of self and matrix B has to match.)rrkrrrr)rMrr5rzs r#rBandedMatrixLU.solve_matrixsb# >>TZZ 'KL L6>mmoFos%%c*oF )+ FsA3)rwrRr?r@rQN)r.rr?rr@rrrr) rrrrrrOrrkrrrrBr<r#rrs)CV## 8r<rc[R"U[RS9nURSn[R"XA4[RS9n[R"U4[R S9nX-S-nUn[ U5HJn [ X- U5Hn X9U X9X- 'M US-n[ Xx- S- U5H n SX9U 'M ML Un[ U5Hn X;Sn U n X:aUS- n[ U S-U5H+n [X:S5[U 5:dM"X:Sn U n M- U S-Xk'X:wa+[ U5Hn X9U X;U sX;U 'X9U 'M [ U S-U5HUn X9SX;S- n XU X- S- '[ SU5Hn X9U XU U -- X9U S- 'M SX9US- 'MW M X5U4$)NrCrror)rErFrGrIrHint64rr) r.r?r@rQr8rRrwmmlr8r<r7dums r#rOrOsXXarzz2E[[^AXXqgRZZ8EXXqd"((3EgkB A 2Yrvr"A#hqkEHQUO# Qrvz2&AEHQK'  A 1Xhqk  5 FAq1uaA58A;#c(*hqk!q5 62Y+08A; ( UXa[q1uaA(1+ +C"%!HQUQY 1b\"'(1+Ahqk0A"AQ""EHR!V  !(  r<cURSnURSU:wa [S5eUnUnXE-S-n Un [U5HWn X;S- n X:wa X X sX 'X 'X:aU S- n [U S-U 5Hn X ==X{X- S- X --ss'M MY Sn [US- SS5HDn X n[SU 5Hn XU U X U ---nM XU S- X 'X:dM?U S- n MF U$)rWrrYror7)rIrr)r[rQrRrwr?r@r8alaurarbr7r<r8rcs r#rZrZ*s/$[[^AwwqzQVWWBBgkB A 1X HqL 6qtJAD!$ 5 FAq1uaA DBE!%!)$qt+ +D!  A 1q5"b !dq!A a58aAh& &CU1X~ 6 FA " Hr<)rzIterable[list])rr%)r7rr8rrr-)rA)r r-r r-r r-rr) r r-r r-r r-rr-rr)r.rrrrr)r.rrrrr)r.r%rrrr) r rr rr rrrrr)T)r.rrztuple[Matrix, int, int])r.rrr)r.rr?rr@rrr)r.r(r?rr@rrz tuple[NDArray, NDArray, NDArray])r[r(rQr(rRr(rwr(r?rr@rrr()6 __future__rtypingrrrrrr r typing_extensionsr r functoolsr itertoolsr r5rbnumpyrE numpy.typingnpt ezdxf.accr__all__r$r-r%__annotations__r&rr'r(rGr1rrABCrrrrrrrrr3rrrrrOrZrBr<r#rss#(   $ T%[) I)#E%*$56)6c?y"[[,,2  3//,R1R1j SWW  P"+\8"9$"B&"BJ7@++ 4+ +\& & "& '2& 7B& & R  $> 8AVAH'T, , ,  ,   , , ,  , r<